-아/어 오다 expresses the idea of a state or an action that is starting to take place and continues. For example:: 가슴이 떨려 와. I'm starting to get nervous. 날이 밝아 온다. "Daytime is starting."

1) 2년 동안 여기에세 살고 있어요 => 2년 동안 여기에서 살고 있어요. 2) 2년 동안 여기에세 살아 왔어요 => 2년 동안 여기에서 살아 왔어요. To me the two sentences are both correct (except 에세) and mean the same thing. If you think like English, #2 may appear more logical but in Korean I think #1 is preferred (simpler). If it is in conversation, one would most likely say "...살았어요". 살았어요 by itself doesn't make it clear whether the speaker is still living there or not, but in real life that sort of thing is already known before the start of the conversation in 99% of the cases. So I would rank it like 1) 살았어요 2) 살고 있어요 3) 살아 왔어요. I feel the same way for the second example. I would prefer 1) 계속 했어요 2) 계 속하고 있어요 3) 계속해 왔어요.